Determining tilt angle of substrate structure using angular Fourier decomposition of scatter image

Abstract

A method includes receiving, by a processing device, a first small angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scattered image of the substrate is collected at a second radiation incidence angle relative to the base of the substrate that is different from the first angle. The method further includes determining a first order Fourier term associated with the first small angle scatter image by performing an angular Fourier decomposition on the first small angle scatter image. The method further includes determining a value of the first angle based on the first order Fourier term.

Description

Technical Field

[0001] The present disclosure relates to methods and systems associated with determining a tilt angle of a structure of a substrate. More specifically, the present disclosure relates to methods and systems for determining a tilt angle of a structure of a substrate using an angular Fourier decomposition of a scattering image of the substrate. Background Art

[0002] The substrate can be produced by a substrate processing process using a substrate processing device. The substrate can include a structure on a substrate base, such as a deposited structure, an etched structure, etc. The structure can extend from the substrate base at an inclined angle. Determining the inclination angle of the structure relative to the substrate can be performed by performing one or more measurements on the substrate including the structure. Summary of the invention

[0003] The following is a simplified overview of the present disclosure in order to provide a basic understanding of some aspects of the present disclosure. The present disclosure is not a broad overview of the present disclosure. It is neither intended to identify the key or important elements of the present disclosure, nor to describe any scope of the specific embodiments of the present disclosure or any scope of the claims. Its sole purpose is to present some concepts of the present disclosure in a simplified form as a preface to a more detailed description presented later.

[0004] In some aspects of the present disclosure, a method includes receiving, by a processing device, a first small-angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scatter image of the substrate is collected at a second angle of incidence of radiation different from the first angle relative to the base of the substrate. The method also includes determining a first-order Fourier term associated with the first small-angle scatter image by performing an angular Fourier decomposition on the first small-angle scatter image. The method also includes determining a value of a first angle based on the first-order Fourier term.

[0005] In another aspect of the present disclosure, a system includes a memory and a processing device coupled to the memory. The processing device is configured to receive a first small-angle scattering image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scattering image of the substrate is collected at a second incident angle of radiation different from the first angle relative to the base of the substrate. The processing device is further configured to determine a first-order Fourier term associated with the first small-angle scattering image by performing an angular Fourier decomposition on the first small-angle scattering image. The processing device is further configured to determine a value of the first angle based on the first-order Fourier term.

[0006] In another aspect of the present disclosure, a non-transitory machine-readable storage medium stores instructions that, when executed, cause a processing device to perform operations including receiving a first small-angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scatter image of the substrate is collected at a second angle of incidence of radiation different from the first angle relative to the base of the substrate. The operations also include determining a first-order Fourier term associated with the first small-angle scatter image by performing an angular Fourier decomposition on the first small-angle scatter image. The operations also include determining a value of the first angle based on the first-order Fourier term. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The present disclosure is illustrated by way of example and not limitation in the figures of the accompanying drawings.

[0008] Figure 1 is a schematic diagram of a system for measuring and analyzing X-rays scattered from a substrate, according to some embodiments.

[0009] Figure 2 is a diagram illustrating a tilt angle of a structure of a substrate according to some embodiments.

[0010] Figure 3 is a graph showing example scattering patterns obtained from a set of incident angles according to some embodiments.

[0011] Figure 4 is a flow chart of a method for determining a tilt angle of a structure of a substrate according to some embodiments.

[0012] Figure 5 is a block diagram illustrating a computer system according to some implementations. DETAILED DESCRIPTION

[0013] Techniques related to the measurement of structures on a substrate are described herein. The substrate may be a semiconductor device. The substrate may have structures thereon. The structures may extend nominally perpendicular to the base of the substrate. Measuring the true angle between the structure and the base of the substrate may be performed by a small angle X-ray scattering method. Details of the asymmetry of the scattering pattern from the small angle X-ray scattering pattern may provide an indication of the angle between the structure on the surface of the substrate and the base of the substrate.

[0014] In some systems, a small angle X-ray scattering (SAXS) method can be used to determine the angle between the structure and the substrate base. The scattering pattern can be used to determine the angle between the structure and the substrate base. The total intensity of the scattering pattern can be used to determine the angle. The total intensity of a portion of the scattering pattern can be used to determine the angle. The total intensity of the scattering pattern outside the masked portion can be used to determine the angle.

[0015] In some systems, SAXS measurements can include providing X-rays to pass through a substrate of interest. Some of the X-ray energy provided to the substrate is scattered into a cone. Energy is collected on the side of the substrate opposite the X-ray source. The collected X-ray energy is used to determine the tilt angle of the structure of the substrate.

[0016] In some systems, SAXS measurements can be performed from multiple X-ray incident angles (e.g., measured as compared to perpendicular to the substrate base). Scanning can be performed along a first dimension. The scan can include multiple measurements, each with a different X-ray incident angle. For example, measurements can be made every 0.1 degree, every 0.2 degree, etc. from the target minimum angle to the target maximum angle. Scattering data can be generated from a large number of angles. For example, scattering data can be generated from 15-40 angles along the first scanning dimension. Further scans can be performed along a second direction. The second direction can be orthogonal to the first direction. Scattering data can also be generated at multiple incident angles in the second scanning dimension.

[0017] The pattern of scattered intensity can be used to determine the angle between the structure and the substrate. An intensity curve can be generated for each scan dimension. The local maximum of the intensity as a function of the angle of incidence can be used to indicate the angle of the structure on the substrate surface. First, sufficient data can be used to generate a sufficiently accurate curve to obtain the desired level of accuracy in two scan dimensions. In some systems, this can include 30-80 total incident angles detected.

[0018] Conventional solutions have many disadvantages. Conventional measurements of the tilt angle of a substrate structure can be time consuming. Between scattering measurements, the substrate is moved relative to the X-ray source, relative to the detection device, etc. The relative motion of the substrate includes motor acceleration, motor deceleration, motion stabilization, etc. Each movement of the substrate relative to the measurement device significantly increases the amount of time spent in the measurement to determine the angle of the substrate structure.

[0019] Some solutions also include collecting large amounts of data that are not used to calculate the tilt angle of the substrate structure. The scatter data includes radial and angular details that are not used in the tilt angle calculation. Conventional solutions that include total intensity integration include inefficiencies in measurement, data storage, data processing, etc.

[0020] The systems and methods of the present disclosure address the above and other disadvantages of conventional solutions. In some embodiments, multiple scattering measurements (SAXS measurements) of a substrate including a structure are performed. Measurements can be performed at a set of incident angles (e.g., various angles between the incident X-rays and the plane of the substrate). A small number of measurements, such as two to eight measurements, can be performed. Scattering patterns are collected. Details of the scattering pattern can be used to determine the tilt angle of the structure on the substrate.

[0021] The scattering pattern is collected from multiple incident angles. The incident angle can be selected to be angle independent, for example, varying along two orthogonal angular dimensions. Details of the scattering pattern (for example, the asymmetry of the scattering pattern) can be exploited to determine the incident angle.

[0022] The scattering pattern may be separated into angular Fourier decomposition components. Angular Fourier decomposition may include separating the scattering pattern into angular Fourier components of various orders (e.g., first order, second order, etc.). Each order Fourier term of the scattering pattern for each incident angle may indicate a tilt angle of a structure on the substrate surface.

[0023] In some embodiments, an averaging strategy may be used to determine the structural tilt angle. The averaging strategy may include calculating the tilt angle of the substrate structure based on each of the one or more Fourier components of each scattering pattern. In some embodiments, an average is found between each of these tilt angles to determine the measured tilt angle of the substrate structure.

[0024] In some embodiments, an intersection strategy may be used to determine the structural tilt angle. In the intersection strategy, a guessed tilt angle may be used. An error term may be defined based on the guessed tilt angle. The error term may include a sum of scattering images, a sum of Fourier terms, etc. The error term may be minimized to determine the tilt angle of the structure of the substrate.

[0025] The methods and systems of the present disclosure provide technical advantages over conventional solutions. Determining the tilt angle of a structure on a substrate may include collecting scattering patterns from multiple incident angles. The number of incident angles may be very small compared to conventional methods. The reduction in incident angles may reduce measurement time, increase measurement throughput, etc.

[0026] Compared to conventional methods, receiving data from fewer incident angles can reduce the data load. Less data can be collected, transmitted, stored, analyzed, etc. Compared to collecting data from a larger number of incident angles in conventional methods such as substrate structure tilt measurement, this can reduce the computational load, data storage and transmission load, etc.

[0027] Improving the accuracy and / or rate of determining the structural tilt angle can improve the substrate processing system. For example, one or more corrective actions can be performed in view of the determined structural tilt angle. Further processing operations of the substrate can be adjusted based on the structural tilt angle. For example, the target processing operation of the subsequent operation on the measured substrate can be adjusted to improve the processing under the measured structural tilt angle. The processing parameters of the etching process (for example, the set points of one or more components for determining the properties of the etching plasma) can be adjusted in view of the measured structural tilt angle. By adjusting the subsequent processing operations of the substrate processing program based on the determined structural tilt angle, the substrate processing system can increase the possibility of producing a substrate that meets one or more target threshold property values. In some embodiments, the processing recipe can be updated based on the structural tilt angle measurement. For example, the measured structural tilt angle may be outside the target threshold range, and the processing recipe can be updated to adjust the tilt angle of the future substrate structure to within the target threshold range. By adjusting the processing recipe, the substrate processing system can increase the possibility of producing a substrate that meets the target performance threshold, which can reduce the costs associated with producing, identifying and discarding defective products. Substrates outside the acceptable range of property values ​​can be effectively identified. For example, substrates having structural tilt angles outside of a threshold range may be quickly and accurately identified, and further processing operations may not be performed, thereby reducing the cost of energy, material, time, environmental impact, etc. of continuing to process substrates predicted to have property values ​​outside of a target range. In some embodiments, tilt angle data may be used to verify the accuracy, reliability, repeatability, etc. of processing steps, operations, substrate designs, etc.

[0028] In some aspects of the present disclosure, a method includes receiving, by a processing device, a first small-angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scatter image of the substrate is collected at a second angle of incidence of radiation different from the first angle relative to the base of the substrate. The method also includes determining a first-order Fourier term associated with the first small-angle scatter image by performing an angular Fourier decomposition on the first small-angle scatter image. The method also includes determining a value of a first angle based on the first-order Fourier term.

[0029] In another aspect of the present disclosure, a system includes a memory and a processing device coupled to the memory. The processing device is configured to receive a first small-angle scattering image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scattering image of the substrate is collected at a second incident angle of radiation different from the first angle relative to the base of the substrate. The processing device is further configured to determine a first-order Fourier term associated with the first small-angle scattering image by performing an angular Fourier decomposition on the first small-angle scattering image. The processing device is further configured to determine a value of the first angle based on the first-order Fourier term.

[0030] In another aspect of the present disclosure, a non-transitory machine-readable storage medium stores instructions that, when executed, cause a processing device to perform operations including receiving a first small-angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first small-angle scatter image of the substrate is collected at a second angle of incidence of radiation different from the first angle relative to the base of the substrate. The operations also include determining a first-order Fourier term associated with the first small-angle scatter image by performing an angular Fourier decomposition on the first small-angle scatter image. The operations also include determining a value of the first angle based on the first-order Fourier term.

[0031] Figure 1 1 is a schematic diagram of a system 100 for measuring and analyzing X-rays scattered from a substrate 102 according to some embodiments. The system 100 can be used to perform small angle X-ray scattering. The system 100 can be used to determine properties of a substrate. The system 100 can be used to determine the tilt angle of a structure of a substrate.

[0032] The substrate 102 can be mounted on a mounting assembly 104. The mounting assembly 104 can be rotated, for example, relative to the incident X-rays 106. The mounting assembly 104 can allow the substrate 102 to be exposed to the X-rays 106 at a range of incident angles. The mounting assembly 104 can be rotated in two dimensions, for example, about a direction perpendicular to the X-rays 106. Figure 1 The axis of the plane (as shown by the curved arrow) rotates and Figure 1 The mounting assembly 104 can rotate about an axis (not shown) in a plane of the mounting assembly 104. The mounting assembly 104 can rotate in an orthogonal dimension. The mounting assembly 104 can rotate about two different axes.

[0033] The X-ray source 108 provides X-rays 106 to the substrate 102. The X-ray source 108 may generate a collimated X-ray beam. The X-ray source 108 may generate a focused X-ray beam. The X-ray source 108 may generate a converging X-ray beam. The X-ray source 108 may include an X-ray tube 110 and one or more optical components 112 (e.g., for shaping the beam).

[0034] When the X-rays 106 interact with the substrate 102 , some scattering of the incident beam occurs. A scattered beam 114 is generated that encodes information about the dimensions of the substrate 102 , including the tilt angle between structures on the substrate 102 and the base of the substrate 102 .

[0035] The scattered beam 114 may be provided to a detector assembly 116. The detector assembly 116 may include a detector array 118. The detector array 118 may provide spatial resolution of the X-ray energy received by the detector assembly 116. The detector array 118 may distinguish angular components of the scattered beam 114. Details of the differences in the responses of the various elements of the detector array 118 may be utilized to determine the tilt angle of the structure of the substrate 102.

[0036] The tilt angle of a structure of a substrate can be determined using a set of incident angles. The set of incident angles can include incident angles that are intended to produce clear intersections of the tilt angles. For example, a substrate having a target or expected tilt angle (usually perpendicular to the base of the substrate) can be measured at a set of incident angles around the expected tilt angle so that the calculated change in direction from the incident angle to the expected tilt angle intersects between the incident angles. Figure 3 The incident angles used to generate the scattering images are discussed in more detail.

[0037] The tilt angle of the structure of the substrate may be determined using the scattering pattern received by the detector array 118. The angular Fourier decomposition of the scattering pattern may indicate the tilt angle of the structure of the substrate.

[0038] Various operations associated with system 100 may be controlled by one or more processing devices (e.g., computing devices). Operations may be performed by dedicated hardware, general-purpose computing devices, computing devices executing dedicated software, and the like. Operations may be performed by devices including computing devices such as personal computers (PCs), laptops, mobile phones, smart phones, tablet computers, netbook computers, network-connected televisions ("smart TVs"), network-connected media players (e.g., Blu-ray players), set-top boxes, over-the-top (OTT) streaming devices, operator boxes, and the like. Devices for performing operations of system 100 may receive user input (e.g., via a graphical user interface (GUI) displayed by one or more devices). Devices of system 100 may perform operations associated with small-angle scattering measurements, data analysis, corrective action recommendations and / or execution, and the like.

[0039] The system 100 includes a control unit 120, which includes a processing device (control processor 122) and a control memory 124. The control unit 120 is communicatively coupled to one or more components of the system 100 for controlling the components of the system. The control unit 120 can be communicatively coupled to the X-ray tube 110, the mounting assembly 103, etc., for example.

[0040] The system 100 includes an analysis unit 130 including a processing device (analysis processor 132) and a memory (analysis memory 134). The analysis unit 130 may perform operations associated with receiving data generated by components of the system 100 and performing analysis on the data. The analysis processor 132 may perform Fourier decomposition on the small angle scattering image. The analysis processor 132 may predict the tilt angle of structures of the substrate based on the small angle scattering measurements generated by components of the system 100.

[0041] Can be combined by Figure 1 For example, the operations of the control processor 122 and the analysis processor 132 may be performed by the same device, or two or more devices may perform the operations belonging to the control unit 120 and the analysis unit 130.

[0042] Figure 2 2 is a diagram showing the tilt angles of structures of a substrate 200 according to some embodiments. The substrate 200 may include a structure array 202. The substrate 200 may further include a substrate base 204.

[0043] The structures of the array of structures 202 may be at a certain tilt angle 206. The tilt angle 206 may be measured relative to a surface of the substrate. The tilt angle 206 may be measured relative to a surface of the substrate base 204. The tilt angle 206 may be measured relative to a plane defined by a portion of the substrate base 204.

[0044] The substrate 200 may be manufactured to have a target tilt angle. The target tilt angle may be 90°, such as Figure 2 As shown. The structure array 202 may have a tilt angle that is different from a target tilt angle. Deviations in the tilt angle from the target tilt angle may be caused by inconsistent manufacturing equipment performance, suboptimal recipe design, suboptimal process chamber constants / settings, etc. In some cases, the tilt angles of the individual structures of the structure array 202 may be substantially the same (e.g., within 0.1 degrees). Determining the tilt angle value may include determining an average tilt value of a probed area of ​​the substrate.

[0045] Figure 3 3 is a diagram showing an example scattering pattern 300 obtained from a set of incident angles according to some embodiments. The scattering pattern 300 is shown on an axis 302. The axis is associated with the angle of an adjustable mounting assembly supporting a substrate during a substrate structure tilt angle measurement. The angle corresponds to adjusting the angle of the mounting assembly to adjust the incident angle of the X-ray used in the substrate structure tilt angle. The first adjustable incident angle and the second adjustable incident angle can be independent, orthogonal, etc.

[0046] A small number of incident angles (e.g., one to eight) may be used to determine the tilt angle of the substrate structure. Figure 3Four scattering patterns 300 are shown in FIG. 3 as an example arrangement for adjustable incident angle measurement.

[0047] In some embodiments, each scattering pattern may include one or more indications of the tilt angle of the structure of the measured substrate. The angular Fourier decomposition component of the scattering pattern may include an indication of the tilt angle of the structure of the measured substrate. The measured incident angle may be selected so that when represented as an ordered pair of a first angle and a second angle, a set of measured angles are not collinear with the predicted structural tilt angle. For example, if the predicted structural tilt angle is within a solid angle range corresponding to the angular space region 304, the measured angle may be selected so that the measured angle is not collinear with the predicted structural tilt angle. The measured angle may be selected so that if one measured angle coincides with the structural tilt angle, at least two other measured angles are not collinear with the structural tilt angle. The measured angle may be selected so that measurements are made at an incident angle shifted from the expected tilt angle in multiple directions. A set of measured angles may be equally shifted from the expected structural tilt angle. For example, an ordered pair representing the values ​​of the first adjustable incident angle and the second adjustable incident angle compared to the expected tilt angle may vary by a certain standard value. The ordered pairs of measurement angles for the four measurement positions may be selected as (0, x), (0, -x), (x, 0), and (-x, 0), where x represents the target angular displacement. The ordered pairs of measurement angles may be selected as Figure 3 , (x, x), (x, -x), (-x, x), and (-x, -x), where x represents a target angular displacement in one angular dimension. In an example system, x can represent half a degree of tilt, and four measurements can be made in angular order of (0.5, 0.5), (0.5, -0.5), (-0.5, 0.5), and (-0.5, -0.5), expressed as tilt compared to a baseline tilt orientation. In some embodiments, the various measured angles may not conform to these values, for example, the measured angles may not be evenly spaced around the expected structural tilt angle, different angle groups or different criteria for angle selection may be utilized, etc.

[0048] One or more of the scattering patterns 300 may be subjected to angular Fourier decomposition. Angular Fourier decomposition may be similar to Fourier techniques used in image processing. Angular Fourier decomposition may include decomposing the scattering pattern into circular periodic component functions. Angular Fourier decomposition may include determining the amplitude and phase of first-order Fourier components (e.g., component functions with frequencies such that a single wavelength corresponds to 360° around a central portion of the scattering pattern). Angular Fourier decomposition may include determining the amplitude and phase of second-order Fourier components (e.g., components with frequencies of component functions such that two wavelengths of the function correspond to 360°). Angular Fourier decomposition may include determining the amplitude and phase of additional Fourier component orders (e.g., third order, fourth order, etc.).

[0049] In some embodiments, the data processing for determining the tilt angle of the structure may include preprocessing. Preprocessing of the data may include outlier removal. Outliers may include abnormal pixel data values, abnormal scatter patterns, etc. Outliers may be rejected for differing from an average or expected value (e.g., a local average of the intensity values ​​of pixels near a potential outlier pixel) by more than a certain number of standard deviations. Excluded pixels may be removed from consideration. Excluded pixels may be replaced with a local average, a value that generates a local smoothing function, etc. Excluded scatter patterns may be removed from consideration of the tilt angle.

[0050] In some embodiments, the central region of the scatter image can be removed from consideration. For example, the central region can correspond to X-ray energy that passes directly through the substrate and may not provide scatter information. A circular block can be applied to the center of the diffraction pattern, for example, defined by a weighted average of the scatter intensities. In some embodiments, preprocessing can include scaling. Scaling can emphasize the importance of data points closer to the center of the scatter pattern. One possible scaling function is

[0051] ,

[0052] where I' is the scaled intensity and I0 is the measured intensity.

[0053] The Fourier decomposition may include calculating the overlap between the measured intensity and a set of Fourier component terms. The Fourier decomposition may include evaluating the overlap angle between the measured intensity and each of the set of Fourier component terms. The overlap integral used to determine the Fourier component terms may have the following form:

[0054]

[0055]

[0056] where I' is the scaled intensity, is the angular coordinate, V n is the magnitude of the target Fourier component in the decomposition, X max and Y max corresponds to the spatial extent of the diffraction image (e.g., pixel counts along the x-axis and y-axis), is the function calculated for each pixel, c x and c y corresponds to the center of the diffraction pattern in the image (e.g., in pixel coordinates), and n is an integer corresponding to the order of the Fourier component. The center point of the diffraction pattern can be determined or calibrated based on the diffraction image of the direct beam without a sample or beam blocker.

[0057] The Fourier components can be associated with the vector representation. The direction of the vector representation can be related to the direction of the tilt angle toward the structure (e.g., compared to the angle of incidence associated with the scattering pattern generated by the measurement of the substrate). The magnitude of the vector representation can be related to the difference between the measured angle and the tilt angle of the structure. In some embodiments, the phase of the Fourier term can determine the tilt angle of the structure of the surface relative to the detection angle (e.g., the measurement angle). The magnitude of the Fourier term can correspond to the confidence that the orientation is correct.

[0058] The Fourier components of the angular Fourier decomposition of the scatter image can correspond to multiple vectors. A first-order Fourier component can correspond to a vector. A second-order Fourier component can correspond to, for example, two vectors pointing in opposite directions. A third-order Fourier component can correspond to three vectors pointing at intervals of 120°, etc. In some embodiments, the direction of the vector associated with the Fourier component can correspond to an amplitude peak in the Fourier component. In some embodiments, the direction of the vector associated with the Fourier component can be aligned with other parts of the Fourier component (such as a valley or a zero crossing). Determining the structural tilt angle based on the Fourier decomposition of the image data can include a correction factor (e.g., on a per-order basis) to ensure that the correct phase is aligned for determining the tilt angle.

[0059] The tilt angle can be determined from the vector of the Fourier components of the angular Fourier decomposition of the scattering pattern using an average-based model. The vector of each order that is most likely to correspond to the direction of the structural tilt angle can be determined. The determination of the appropriate vector from each Fourier component can be performed by determining which vector is most likely based on other vectors of the same scattering image. The determination of the appropriate vector from each Fourier component can be based on the vectors of other scattering images of the same substrate. Determining which vectors of a set of Fourier components from the scattering image can be based on the magnitude of the vector combination associated with the scattering image. For example, a first-order vector can be added to each of the two second-order vectors. The resulting vector with a larger magnitude can be considered to be associated with the correct second-order vector. The vector magnitude can be related to the tilt magnitude (for example, by calibrating for one or more known samples). The tilt angle of the structure of the substrate can be determined using the average tilt corresponding to each of a set of Fourier components from each of a set of scattering patterns.

[0060] The tilt angle may be determined using an intersection-based model. The intersection model may include determining an intersection point of vector directions indicated by a plurality of scatter patterns associated with a plurality of measured incident angles. The intersection model may determine an optimal or average intersection point of vectors indicating the tilt angle of the structure.

[0061] In some embodiments, an error-based model can be used to determine the structural tilt angle from the scattering pattern. A guess for the structural tilt angle can be determined. The guess can be random, can be an expected tilt angle, etc. An error function can be defined and evaluated based on the guess value. The error function can include a sum of Fourier orders. The error function can include a sum of scattering patterns. The error function can include a term that reduces the weight of scattering patterns associated with measured angles close to the tilt angle (e.g., to reduce noise in the intersection-based model). In some embodiments, in the intersection-based tilt angle determination, scattering data obtained at an incidence angle near the structural tilt angle (e.g., within a threshold angular distance from the structural tilt angle, as predicted by other scattering images from other incidence angles) can be rejected based on calculation.

[0062] A simple example error term may have the following form:

[0063] ,

[0064] Where E is the error, A i is the incident angle of the scatter image, F is the Fourier component of the Fourier decomposition of the calculated scatter image, is a guess about the tilt angle, is the tilt angle calculated based on Fourier decomposition. The error term can take advantage of additional components to provide better performance. For example, a more complex error term can have the following form:

[0065] ,

[0066] Where E is the error, A i is the incident angle of the scatter image, F is the Fourier component of the Fourier decomposition of the calculated scatter image, is a guess about the tilt angle, is the tilt angle calculated based on Fourier decomposition, and C is a cutoff term designed to reduce the impact of scattering images obtained with incident angles too close to the tilt angle of the structure to make the data meaningful. This second error term can improve the performance by attenuating scattering images with incident angles close to the tilt angle of the structure of the substrate, and attenuates the contribution of large tilt angles to the error term compared to the simple error term.

[0067] Any convenient minimization process can be used to minimize the error term. The minimization process can include an exhaustive search for possible tilt angle guesses. The minimization process can include a genetic minimization operation. Any other type of minimization process can be used to find the tilt angle with the smallest error term. The tilt angle that minimizes the error term can be the calculated tilt angle of the structure of the substrate.

[0068] Figure 44 is a flow chart of a method 400 for determining a tilt angle of a structure of a substrate according to some embodiments. The method 400 may be performed by processing logic, which may include hardware (circuitry, dedicated logic, etc.), software (e.g., instructions running on a processing device), or a combination thereof. In one embodiment, some or all of the operations of the method 400 may be performed by Figure 1 In some embodiments, one or more operations of method 400 may be performed by one or more components of system 100. Figure 1 The operations of method 400 may be performed by the processing device shown in Figure 1 The analysis processor 132 of the analysis unit 130 executes.

[0069] At block 410, processing logic receives a first low-angle scatter image of a substrate. The substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate. The first low-angle scatter image of the substrate is collected at a second incident angle of radiation different from the first angle relative to the base of the substrate.

[0070] In some embodiments, a second small angle scatter image may be received. The second small angle scatter image may be an image of the same substrate. The second small angle scatter image may be collected at a third angle of incidence of radiation relative to a base of the substrate that is different from the second angle.

[0071] At block 412, processing logic determines a first first-order Fourier term associated with the first small-angle scatter image by performing angular Fourier decomposition on the first small-angle scatter image. The processing logic may also determine a first second-order Fourier term associated with the first small-angle scatter image. The processing logic may also determine a second first-order Fourier term associated with the second small-angle scatter image. The processing logic may also determine a second second-order Fourier term associated with the second small-angle scatter image.

[0072] At block 414, processing logic determines a value of the first angle based on the first first-order Fourier term. Determining the first angle (e.g., the orientation of the structure relative to the substrate base) may be further based on the second first-order Fourier term. Determining the first angle may be further based on the first second-order Fourier term. Determining the first angle may be further based on the second second-order Fourier term.

[0073] Determining the first angle may include generating a vector representation corresponding to one or more Fourier terms. Determining the first angle may include generating a vector representation corresponding to one or more of a first first-order Fourier term, a second first-order Fourier term, a first second-order Fourier term, or a second second-order Fourier term. Determining the first angle may also include determining which component of each vector representation is used to determine the first angle. The second-order Fourier term may be associated with two vectors, one of which may be used to determine the first angle. Determining the first angle may include determining a first additive combination of vectors associated with the first small-angle scatter image. The first additive combination of vectors may include vectors associated with the first first-order Fourier term and the first second-order Fourier term. The additive combination of vectors may include one vector for each Fourier term from the first small-angle scatter image to be used to determine the first tilt angle. The first additive combination of vectors may be selected so that it has the maximum magnitude among all possible additive combinations of vectors including one vector for each Fourier term from the first small-angle scatter image to be used to determine the first tilt angle. Determining the first angle may also include determining a second additive combination of vectors associated with the second small-angle scatter image. The second additive combination of vectors may be generated in a manner similar to the first additive combination of vectors. Determining the first angle may also include determining a first tilt angle indicated by the first additive combination of vectors. Determining the first angle may also include determining a second tilt angle associated with the second additive combination of vectors. Determining the value of the first angle may be based on the first tilt angle and the second tilt angle.

[0074] In some embodiments, determining the value of the first angle may further include determining a guess value for the value of the first angle. Determining the value of the first angle may further include determining an error based on the guess value. Determining the value of the first angle may include determining an error for each of a plurality of small-angle scatter images based on the guess value. Determining the value of the first angle may include determining an error for each of a plurality of Fourier components based on the guess value. Determining the value of the first angle may include determining an error for each of a plurality of Fourier components for each of a plurality of small-angle scatter images based on the guess value. Determining the value of the first angle may include determining an error for each of a plurality of Fourier components for each of a plurality of small-angle scatter images based on the guess value. Determining the value of the first angle may include determining a first error based on the guess value and a first first-order Fourier term, determining a second error based on the guess value and a first second-order Fourier term, determining a third error based on the guess value and a second first-order Fourier term, and determining a fourth error based on the guess value and a second second-order Fourier term. Determining the value of the first angle may include determining an optimized value for the first angle that minimizes a combined error term. Determining the value of the first angle may include determining an optimized value that minimizes a sum of the individual errors. Error determination may include determining a scaling term. Error determination may include determining a cutoff term. If the incident angle of the small-angle scatter image is similar to the first angle, the cutoff term may reduce the weight of the data associated with the small-angle scatter image. If the first angle is similar to the third angle (eg, within a threshold), the cutoff term may reduce the weight of data associated with a second low-angle scattering image of the substrate.

[0075] Figure 5 5 is a block diagram illustrating a computer system 500 according to some embodiments. In some embodiments, the computer system 500 can be connected (e.g., via a network, such as a local area network (LAN), an intranet, an extranet, or the Internet) to other computer systems. The computer system 500 can operate as a server or client computer in a client-server environment, or as a peer computer in a peer-to-peer or distributed network environment. The computer system 500 can be provided by a personal computer (PC), a tablet PC, a set-top box (STB), a personal digital assistant (PDA), a cellular phone, a network device, a server, a network router, a switch or a bridge, or any device capable of executing a set of instructions (sequential or otherwise) specifying an action to be taken by the device. In addition, the term "computer" should include any collection of computers that execute a set (or multiple sets) of instructions individually or jointly to perform any one or more methods described herein.

[0076] In another aspect, the computer system 500 may include a processing device 502 , a volatile memory 504 (e.g., a random access memory (RAM)), a nonvolatile memory 506 (e.g., a read only memory (ROM) or an electrically erasable programmable ROM (EEPROM)), and a data storage device 518 that may communicate with each other via a bus 508 .

[0077] The processing device 502 may be provided by one or more processors, such as a general purpose processor (such as, for example, a complex instruction set computing (CISC) microprocessor, a reduced instruction set computing (RISC) microprocessor, a very long instruction word (VLIW) microprocessor, a microprocessor that implements other types of instruction sets, or a microprocessor that implements a combination of instruction set types) or a special purpose processor (such as, for example, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), or a network processor).

[0078] Computer system 500 may also include a network interface device 522 (eg, coupled to network 574). Computer system 500 may also include a video display unit 510 (eg, LCD), an alphanumeric input device 512 (eg, keyboard), a cursor control device 514 (eg, mouse), and a signal generating device 520.

[0079] In some embodiments, the data storage device 518 may include a non-transitory computer-readable storage medium 524 (e.g., a non-transitory machine-readable medium) on which instructions 526 encoding any one or more of the methods or functions described herein may be stored, including instructions for executing in conjunction with Figure 3-Figure 4 The described operations are associated and instructions for encoding components for implementing the methods described herein. The instructions 526 may include a tilt angle determination component 550 for determining a tilt angle of a structure of a substrate.

[0080] The instructions 526 may also reside, completely or partially, within the volatile memory 504 and / or within the processing device 502 during execution by the computer system 500, and thus, the volatile memory 504 and the processing device 502 may also constitute machine-readable storage media.

[0081] Although the computer-readable storage medium 524 is shown as a single medium in the illustrative example, the term "computer-readable storage medium" shall include a single medium or multiple media (e.g., a centralized or distributed database and / or associated caches and servers) that store one or more sets of executable instructions. The term "computer-readable storage medium" shall also include any tangible medium that can store or encode a set of instructions for execution by a computer, the instructions causing the computer to perform any one or more of the methods described herein. The term "computer-readable storage medium" shall include, but is not limited to, solid-state memories, optical media, and magnetic media.

[0082] The methods, components, and features described herein may be implemented by discrete hardware components, or may be integrated into the functionality of other hardware components such as ASICs, FPGAs, DSPs, or similar devices. In addition, the methods, components, and features may be implemented by firmware modules or functional circuits within a hardware device. Furthermore, the methods, components, and features may be implemented in any combination of hardware devices and computer program components or in a computer program.

[0083] Unless otherwise specifically stated, terms such as "receive," "perform," "provide," "obtain," "cause," "access," "determine," "add," "use," "train," "reduce," "generate," "correct," and the like refer to actions and processes performed or implemented by a computer system that manipulates and converts data represented as physical (electronic) quantities within computer system registers and memories into other data similarly represented as physical quantities within computer system memories or registers or other such information storage, transmission, or display devices. In addition, the terms "first," "second," "third," "fourth," and the like as used herein are intended as labels to distinguish between different elements and may not have ordinal meanings according to their numerical labels.

[0084] The examples described herein also relate to an apparatus for performing the methods described herein. The apparatus may be specially constructed to perform the methods described herein, or it may include a general-purpose computer system selectively programmed by a computer program stored in the computer system. Such a computer program may be stored in a computer-readable tangible storage medium.

[0085] The methods and illustrative examples described herein are not inherently related to any particular computer or other device. Various general purpose systems may be used in accordance with the teachings described herein, or it may prove convenient to construct more specialized devices to perform the methods described herein and / or each of their respective functions, routines, subroutines, or operations. Examples of the structures of various such systems are set forth in the description above.

[0086] The above description is intended to be illustrative rather than restrictive. Although the present disclosure has been described with reference to specific illustrative examples and embodiments, it should be appreciated that the present disclosure is not limited to the described examples and embodiments. The scope of the present disclosure should be determined with reference to the following claims and the full scope of equivalents to which the claims are entitled.

Claims

1. A method comprising: receiving, by a processing device, a first small angle scatter image of a substrate, wherein the substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate, and wherein the first small angle scatter image of the substrate is collected at a second angle of incidence of radiation relative to the base of the substrate that is different from the first angle; performing, by the processing device, angular Fourier decomposition on the first small-angle scatter image to determine a first-order Fourier term associated with the first small-angle scatter image; as well as The value of the first angle is determined by the processing device based on the first-order Fourier term.

2. The method of claim 1, further comprising determining a first second-order Fourier term by performing Fourier decomposition on the first small-angle scatter image, wherein the step of determining the value of the first angle is further based on the first second-order Fourier term.

3. The method according to claim 1, further comprising: receiving a second small angle scatter image of the substrate, wherein the second small angle scatter image of the substrate is collected at a third angle of incidence of the radiation relative to a base of the substrate; and A second first order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein the step of determining the value of the first angle is further based on the second first order Fourier term.

4. The method according to claim 3, further comprising: determining a first second-order Fourier term by performing angular Fourier decomposition on the first small-angle scatter image; as well as A second second order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein the step of determining the value of the first angle is further based on the first second order Fourier term and the second second order Fourier term.

5. The method according to claim 4, further comprising: Generate a vector representation of each of the following: The first first-order Fourier term, The first second-order Fourier term, the second first-order Fourier term, and The second second-order Fourier term; determining a first additive combination of vectors associated with the first small-angle scatter image, wherein the first additive combination of vectors includes one vector component from each of the first first-order Fourier term and the first second-order Fourier term, and wherein the first additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the first first-order Fourier term and the first second-order Fourier term; determining a second additive combination of vectors associated with the second small-angle scatter image, wherein the second additive combination of vectors includes one vector component from each of the second first-order Fourier term and the second second-order Fourier term, and wherein the second additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the second first-order Fourier term and the second second-order Fourier term; determining a first tilt angle associated with a first additive combination of the vectors; as well as A second tilt angle associated with a second additive combination of the vectors is determined, wherein the step of determining the value of the first angle is based on the first tilt angle and the second tilt angle.

6. The method according to claim 4, further comprising: determining a guess of the value of the first angle; determining an error for each of the first first-order Fourier term, the second first-order Fourier term, the first second-order Fourier term, and the second second-order Fourier term based on the guess value; as well as An optimized value for the first angle is determined that minimizes a sum of the errors associated with the first first-order Fourier term, the first second-order Fourier term, the second first-order Fourier term, and the second second-order Fourier term.

7. The method of claim 6, wherein the error includes a cutoff term that reduces the weight of data associated with the second low-angle scatter image when the value of the third angle of incidence is within a threshold difference of the value of the first angle.

8. A system comprising a memory and a processing device coupled to the memory, wherein the processing device is configured to: receiving a first small angle scattering image of a substrate, wherein the substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate, and wherein the first small angle scattering image of the substrate is collected at a second angle of incidence of radiation relative to the base of the substrate that is different from the first angle; determining a first-order Fourier term associated with the first small-angle scatter image by performing angular Fourier decomposition on the first small-angle scatter image; and A value of the first angle is determined based on the first-order Fourier term.

9. The system of claim 8, wherein the processing device is further configured to determine a first second-order Fourier term by performing Fourier decomposition on the first small-angle scattering image, wherein determining the value of the first angle is further based on the first second-order Fourier term.

10. The system according to claim 8, wherein the processing device is further configured to: receiving a second small angle scatter image of the substrate, wherein the second small angle scatter image of the substrate is collected at a third angle of incidence of the radiation relative to a base of the substrate; and A second first order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein determining the value of the first angle is further based on the second first order Fourier term.

11. The system according to claim 10, wherein the processing device is further configured to: determining a first second-order Fourier term by performing angular Fourier decomposition on the first small-angle scatter image; and A second second order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein determining the value of the first angle is further based on the first second order Fourier term and the second second order Fourier term.

12. The system according to claim 11, wherein the processing device is further configured to: Generate a vector representation of each of the following: The first first-order Fourier term, The first second-order Fourier term, The second first-order Fourier term, and The second second-order Fourier term; determining a first additive combination of vectors associated with the first small-angle scatter image, wherein the first additive combination of vectors includes one vector component from each of the first first-order Fourier term and the first second-order Fourier term, and wherein the first additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the first first-order Fourier term and the first second-order Fourier term; determining a second additive combination of vectors associated with the second small-angle scatter image, wherein the second additive combination of vectors includes one vector component from each of the second first-order Fourier term and the second second-order Fourier term, and wherein the second additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the second first-order Fourier term and the second second-order Fourier term; determining a first tilt angle associated with a first additive combination of the vectors; and A second tilt angle associated with a second additive combination of the vectors is determined, wherein determining the value of the first angle is based on the first tilt angle and the second tilt angle.

13. The system according to claim 11, wherein the processing device is further configured to: determining a guess of the value of the first angle; determining an error for each of the first first-order Fourier term, the second first-order Fourier term, the first second-order Fourier term, and the second second-order Fourier term based on the guess value; and An optimized value for the first angle is determined that minimizes a sum of the errors associated with the first first-order Fourier term, the first second-order Fourier term, the second first-order Fourier term, and the second second-order Fourier term.

14. The system of claim 13, wherein the error comprises a cutoff term that reduces the weight of data associated with the second low-angle scatter image when the value of the third angle of incidence is within a threshold difference of the value of the first angle.

15. A non-transitory machine-readable storage medium storing instructions that, when executed, cause a processing device to perform operations comprising: receiving a first small angle scattering image of a substrate, wherein the substrate includes a plurality of structures oriented at a first angle relative to a base of the substrate, and wherein the first small angle scattering image of the substrate is collected at a second angle of incidence of radiation relative to the base of the substrate that is different from the first angle; determining a first-order Fourier term associated with the first small-angle scatter image by performing angular Fourier decomposition on the first small-angle scatter image; as well as The value of the first angle is determined based on the first-order Fourier term.

16. The non-transitory machine-readable storage medium of claim 15, the operations further comprising: A first second order Fourier term is determined by performing Fourier decomposition on the first small angle scatter image, wherein determining the value of the first angle is further based on the first second order Fourier term.

17. The non-transitory machine-readable storage medium of claim 15, the operations further comprising: receiving a second small angle scatter image of the substrate, wherein the second small angle scatter image of the substrate is collected at a third angle of incidence of the radiation relative to a base of the substrate; and A second first order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein the step of determining the value of the first angle is further based on the second first order Fourier term.

18. The non-transitory machine-readable storage medium of claim 17, the operations further comprising: determining a first second-order Fourier term by performing angular Fourier decomposition on the first small-angle scatter image; as well as A second second order Fourier term is determined by performing angular Fourier decomposition on the second small angle scatter image, wherein determining the value of the first angle is further based on the first second order Fourier term and the second second order Fourier term.

19. The non-transitory machine-readable storage medium of claim 18, the operations further comprising: Generate a vector representation of each of the following: The first first-order Fourier term, The first second-order Fourier term, the second first-order Fourier term, and The second second-order Fourier term; determining a first additive combination of vectors associated with the first small-angle scatter image, wherein the first additive combination of vectors includes one vector component from each of the first first-order Fourier term and the first second-order Fourier term, and wherein the first additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the first first-order Fourier term and the first second-order Fourier term; determining a second additive combination of vectors associated with the second small-angle scatter image, wherein the second additive combination of vectors includes one vector component from each of the second first-order Fourier term and the second second-order Fourier term, and wherein the second additive combination of vectors has a maximum magnitude among all additive combinations of vectors that include one vector component from each of the second first-order Fourier term and the second second-order Fourier term; determining a first tilt angle associated with a first additive combination of the vectors; as well as A second tilt angle associated with a second additive combination of the vectors is determined, wherein determining the value of the first angle is based on the first tilt angle and the second tilt angle.

20. The non-transitory machine-readable storage medium of claim 18, the operations further comprising: determining a guess at the value of the first angle; determining an error for each of the first first-order Fourier term, the second first-order Fourier term, the first second-order Fourier term, and the second second-order Fourier term based on the guess value; as well as An optimized value for the first angle is determined that minimizes a sum of the errors associated with the first first-order Fourier term, the first second-order Fourier term, the second first-order Fourier term, and the second second-order Fourier term.

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